If the diameter of the earth becomes two times its present value and its mass remain unchanged then how would the weight of an object on the surface of the Earth be affected??
Answers
Answer:
Acceleration due to gravity is g=
R
2
GM
=
(
2
D
)
2
GM
=
D
2
4GM
Where,G=Universal gravitational constant
M=mass of the Earth
R=radious of the Earth
D=Diameter of the Earth
Now,g
′
=
(
2
D
)
2
GM
=
D
2
GM
=
4
g
Weight of the body=mg
′
=
4
mg
If diameter is doubled then radius is also doubled, i.e, the distance of the object from the center doubles. We know that weight is inversely proportional to the square of the distance, so weight reduces to one fourth its original value.
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Explanation:
If diameter is doubled then radius is also doubled, i.e, the distance of the object from the center doubles. We know that weight is inversely proportional to the square of the distance, so weight reduces to one fourth its original value.
Using F = G M m R 2 GMmR2 we have new weight given by F' = G M m ( 2 R ) 2 GMm(2R)2 = 1 4 14F ∴ ∴ Weight becomes one-fourth of the original value.
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